"For example; Koshi nage is a very general term, it simply means "hip throw". That name points to a thing, the thing is someone being thrown by way of the hip. Now off the top of my head, I can think of about 5 distinctly different ways to accomplish that task. Those ways are all different and so might be the names by which I call them. But the end result is the same; someone got thrown by way of my hip."

I do not think that the fact that a technique has a descriptive name gives you a license to make it up. Let me rephrase it, the name denotes a specific technique. You can make up stuff five or 25 ways that satisfying the name, that does not make them valid Aikido. O-Goshi is a great Judo technique (http://uk.youtube.com/watch?v=9UZ02P8M10c) but wearing a hakama while doing it does not make it Aikido. Here for example http://uk.youtube.com/watch?v=9UZ02P8M10c (starting at about 3:40), Saito demonstrates, why is important to be able to turn towards your blind spot once the throw is completed. This approach allows for multiple attackers and indicates true Aikido quality.

Quote:

"I guess it depends whether your interest is in the overall effect or the specifics that led up to that effect."

You are right, in one case you get cut from behind by the other attacker and in the other you do not.